The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  X  1  1  1  1  1  X  1
 0 X^2  0  0  0  0  0  0  0  0 X^2 2X^2 2X^2 X^2 X^2 X^2  0 2X^2 2X^2 X^2 X^2 X^2  0 X^2 X^2  0 2X^2 2X^2 2X^2 X^2 X^2 X^2  0 X^2  0  0 2X^2  0 2X^2 2X^2 X^2 X^2 X^2 X^2  0  0 2X^2 2X^2 2X^2 X^2  0
 0  0 X^2  0  0  0  0 X^2 2X^2 2X^2 2X^2  0  0 2X^2 X^2 2X^2 X^2  0 X^2 X^2 X^2  0 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 X^2 2X^2 X^2 X^2  0 X^2 X^2  0 2X^2 X^2 X^2  0 2X^2 2X^2 2X^2 X^2 2X^2 2X^2
 0  0  0 X^2  0  0 X^2 2X^2  0 2X^2  0  0 2X^2 X^2 X^2 2X^2  0 X^2 2X^2 2X^2 2X^2 X^2 X^2 2X^2 2X^2 2X^2 X^2  0 X^2  0 2X^2  0 X^2 X^2 2X^2 X^2 2X^2 X^2 2X^2 X^2 2X^2 X^2 X^2 X^2 X^2 X^2  0 2X^2 2X^2 X^2 X^2
 0  0  0  0 X^2  0 2X^2 2X^2 X^2  0 2X^2 2X^2 2X^2  0 2X^2 2X^2  0 2X^2 2X^2 X^2  0  0 2X^2  0 2X^2 2X^2 X^2 2X^2 2X^2  0  0 2X^2  0 X^2 X^2  0 X^2 2X^2  0  0 X^2 2X^2 X^2 X^2 X^2 2X^2  0  0  0 2X^2 X^2
 0  0  0  0  0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 X^2  0 2X^2 2X^2  0  0  0 2X^2 X^2  0  0 2X^2 X^2 X^2  0  0  0 2X^2 X^2 X^2  0  0  0 X^2  0 2X^2  0 2X^2 2X^2  0 2X^2 2X^2 2X^2 X^2

generates a code of length 51 over Z3[X]/(X^3) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+54x^90+134x^93+18x^94+98x^96+144x^97+100x^99+432x^100+4442x^102+576x^103+58x^105+288x^106+52x^108+42x^111+44x^114+32x^117+22x^120+14x^123+4x^126+4x^129+2x^141

The gray image is a linear code over GF(3) with n=459, k=8 and d=270.
This code was found by Heurico 1.16 in 0.312 seconds.